Taylor polynomial remainder (part 2) | Series | AP Calculus BC | Khan Academy
Why Mathematics Stack Exchange recommends it
Mathematics Stack Exchange users link it when someone needs to understand why the Taylor remainder or error term takes the form it does, and sometimes as a general calculus reference.
Recommended by 2 people across 2 different months, 2017 to 2021.
What it is
Sal Khan proves the Lagrange error bound for Taylor polynomial approximations, showing how far a Taylor polynomial can be from the function it approximates. It is part 2 of a two-part lesson in Khan Academy's AP Calculus BC series unit, taught as a whiteboard-style walkthrough.
What people said
Recommends Aaron Quitta · 2018-08 · Mathematics Stack Exchange · on “Constructing a numerical proof that integration is equivalent to antidifferentiation”
Oh, I am wholly unfamiliar and the Wikipedia article is a little much for me. I found a Khan Academy, here [this video] , video which seems to cover the relevant topic. But I'm of how to apply it our context. I'm sorry for the wholes in my knowledge, I've foucused on systematically/offically learning calculus.
Recommends SAGALPREET SINGH · 2021-06 · Mathematics Stack Exchange · on “Taylor Series Expansion only upto two terms.”
In addition to what @Stuck mentioned, this video [this video] might help in clarifying why and how the error term (remainder term) is that.
Cites Mattias Johnson · 2017-11 · Mathematics Stack Exchange · on “Is the anti-derivative of $f'(x) = f(x)$ OR $f(x) + C$”
Pretty straightforward question from the title. What is the anti-derivative of $f'(x)$? In my head it makes sense for it to be $f(x) + C$ since I can take the derivative of that and get back to where I started, I however noticed in Khan Academy's video [this video] that he claims it's $f(x)$